Edge Sliding multiple verts/edges along a single edge axis?
The easiest way is to create a custom transform.
Select an edge that represents the orientation of your desired transform, in your case, this will be where the red arrow is pointing, then Ctrl + Alt +  Space bar  this will create custom transform using the orientation of the selected edge, now you can use this new transform to move your mesh along. For example if you want to move the selected vertices/edges/faces on the new Y axis, select them, press G to move, then press Y + Y, this will change the orientation from the default Global to the new custom transform. You can edit the parameters of your custom transform immediately after creating it in the tool's   shelf to the left of the 3D view, if you can't see it use T to show it. You can rename and delete the custom transform in the properties shelf to the right of your 3D view, use N to toggle it's visibility.